Mobile-Edge Computing (MEC) is about offering application developers and service providers cloud-computing capabilities and an IT service environment at the edge of the mobile network. However, although cloud computing can be used to meet traditional challenges, like scalability concerns and provide for fast resource provisioning times, a multifaceted analysis is required when it comes in multi-operator environments with time-critical applications and services. In this work, we claim that the service importance must be at the epicenter when it comes to the scheduling and placement decision of whether to deploy the service at the edge network or not. Virtual machine (VM) scheduling decisions should avoid SLA violations for popular or time-critical services, and be fair between the service providers. A Lyapunov optimization framework is derived to solve this stochastic optimization problem that aims to maximize the revenue of the physical infrastructure owner in a multi-network operator-sharing environment with time-critical SLAs. A series of simulation experiments validate the high effectiveness of the proposed approach over benchmarking ones.